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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 232 (page 695)

For rational function, $f (x) = \frac{x + 1}{x^{2} - 2 x - 3}$ ,
a) find the domain of the function
b) solve f(x) = 1
c) find the points on the graph at this function value.

Short Answer

Expert verified

a) The domain is all real numbers except $3, - 1$ .

b) The solution is $x = 4$ .

c) The point is $(4, 1)$ .

Step by step solution

01

(a)Step 1. Given

The given function is $f (x) = \frac{x + 1}{x^{2} - 2 x - 3}$

02

Step 2. To find

Find the domain of the function.

03

Step 3. Calculation

For the domain, the denominator can not be 0.

$x^{2} - 2 x - 3 鈮� 0 (x - 3) (x + 1) 鈮� 0 x 鈮� 3, - 1$

04

(b)Step 1. Given

The given function is $f (x) = \frac{x + 1}{x^{2} - 2 x - 3}$

05

Step 2. To find

Solve $f (x) = 1$ .

06

Step 3. Calculation

Set the given equation equal to 1 and solve for x.

$\frac{x + 1}{x^{2} - 2 x - 3} = 1 x + 1 = x^{2} - 2 x - 3 x^{2} - 3 x - 4 = 0 (x - 4) (x + 1) = 0 x = 4, - 1$

But $x 鈮� - 1$ , so $x = 4$ .

07

(c)Step 1. Given

The given function is $f (x) = \frac{x + 1}{x^{2} - 2 x - 3}$

08

Step 2. To find

Find the points on the graph at this function value.

09

Step 3. Calculation

The value of x is 4.

The value of y is 1.

So, the point is $(4, 1)$

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Most popular questions from this chapter

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